       Re: Partial Differential Equation

• To: mathgroup at smc.vnet.net
• Subject: [mg26660] Re: Partial Differential Equation
• From: "Kevin J. McCann" <KevinMcCann at home.com>
• Date: Wed, 17 Jan 2001 00:47:16 -0500 (EST)
• References: <93r7gq\$4q4@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Philippe,

The problem you have posed is a 2-point boundary value problem which Mathematica
often has difficulty with. The solution is to turn it into a one-point BVP,
and find the initial condition on T(0) that gives the desired T'(1). The
technique is often called a shooting technique.

I have sent you a NB separately that gives my attempt.

Cheers,

Kevin

The wise words of P. Poinas on 13 Jan 2001 22:47:38 -0500:

> Dear Group,
>
> I am trying to solve the following problem:
>
> \!\(\(\(NDSolve[{\(T''\)[R] + \((1/\((R + 0.05)\))\)\ \(T'\)[R] -
>           10\^\(-8\)\ \ T[R]\^4 == 0, \(T'\) == \(-0.07\), \
> \(T'\) ==
>         0}, \ T, \ {R, \ 0, \ 1}]\)\(\ \)\)\)
>
> and I get the following message:
>
> NDSolve::"inrhs": "Differential equation does not evaluate to a number
> or the \
> equation is not an nth order linear ordinary differential equation."
>
> I know that this error is because I am defining the derivative at 2
> different R values:
>
> at R=0, T'[0 ]= -0.07
> and R=1, T' = 0
>
> hence it is not an initial boundary condition.
>
> 1) How can I turn around the problem?
>
>
> Actually, I found the Mathematica Book (V4) very weak on the subject. In
> page 924, it seems possible in In to find a solution to a linear
> differential equation, even with 2 boundary conditions defined at 2
> different x values! My problem being not linear cannot therefore be
> solved. But Mathematica does not mentioned the linearity as a show
> stopper.
>
> 2) Does anybody know a better description of Mathematica's capacity?
>
>         Thank you for helping me,
>
>
>                         Philippe Poinas
>
>

```

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